Wadsworth, who was jeered by the home support on his first return to the Galpharm Stadium since being sacked in 2003, won a tactical battle with young manager Lee Clark.
The experienced coach, who was famously sacked then re-instated because Town could not afford to pay him off, sent out his team with just one forward up front and ensured 10 men were behind the ball at all times.
Town were in charge only to be mugged two minutes before the break when Leon McSweeney grabbed what proved to be the only goal of the game.
In the second half Clark, who played under Wadsworth for England Under-20s two decades ago, threw caution to the wind, playing three up front and three at the back.
But Hartlepool, with five wins in their previous six matches, are growing in confidence under Wadsworth, in charge until the end of the season after Chris Turner's resignation.
Town dominated the first half but the final pass was lacking and strikers Jordan Rhodes and Joe Garner were starved of service.
Graham Carey sent a free-kick over the top then Anthony Pilkington, celebrating a two-year contract extension, started and finished a sweeping move but young goalkeeper Jake Kean pulled off a good save.
Gary Roberts whipped a cross in for Rhodes but his flick across the face of goal was just out of reach for Pilkington.
Kean dived in to deny Roberts before Rhodes's acrobatic shot came back off Antony Sweeney.
Despite having just James Brown as a lone frontman, Hartlepool showed enough in attack to worry Town's bench.
McSweeney struck when he finished off Evan Horwood's cross at the far post and that ultimately proved enough.
Hartlepool made Town battle every step of the way in the second half, and Kean, on loan from Blackburn Rovers, stood firm, snatching every ball as if his life depended on it.
Rhodes fired over before Roberts also wasted a chance and, in truth, Town did not create the chances their possession warranted.
With 20 minutes left, Clark pushed Rhodes, Benik Afobe and Lee Novak up front but the visiting defence was rock solid.
Kean denied Novak and Peter Clarke and Town had an escape when substitute Colin Larkin missed an open goal five minutes from time.
Three minutes later Kean produced the save of the day to keep out Pilkington's powerful effort and it was all over for Town.
Clark said: "All in all it was a shocking Boxing Day. We missed a great chance to go into the top two.
"I don't believe any of my players performed to their full potential."
Huddersfield Town: Smithies; Arfield, McCombe, P Clarke, Carey (Lee 90); Pilkington, Gudjonsson (Novak 69), Kay, Roberts; Garner (Afobe 55), Rhodes. Unused substitutes: Bennett, T Clarke, Atkinson, N Clarke.
Hartlepool United: Kean; Austin, Collins, Hartley, Horwood; Murray (Haslam 73); McSweeney (Bjornsson 83), Liddle, Monkhouse; Sweeney; Brown (Larkin 60). Unused substitutes: Rafferty, Humphreys, Gamble, Yantorno.
Referee: M A Naylor (South Yorks)